Section: New Results

An averaging technique for highly-oscillatory Hamiltonian problems.

Participants : François Castella, Philippe Chartier, Erwan Faou.

In this work [11] , we are concerned with the numerical solution of highly-oscillatory Hamiltonian systems with a stiff linear part. We construct an averaged system whose solution remains close to the exact one over bounded time intervals, possesses the same adiabatic and Hamiltonian invariants as the original system, and is non-stiff. We then investigate its numerical approximation through a method which combines a symplectic integration scheme and an acceleration technique for the evaluation of time-averages developped in an earlier work by the authors. Eventually, we demonstrate the efficiency of our approach on two test problems with one or several frequencies.